Question

NEED HELP ASAP

if f(x)=sqrt x-3 and g(x)=1-x^2 then what did you notice about the domain of (f o g)(x)?

Answer 1

The domain of f, and thus the range of g, is restricted to values greater than or equal to 3.

If 1 minus x squared is greater than or equal to 3, then x squared must be less than –2.

Since x squared cannot be less than a negative number, the function is undefined for all values of x.

Explanation:

Answer 2

The domain is an empty set

EXPLANATION

The given functions are:

`f(x) = √(x - 3)`

and

`g(x) =1 - {x}^(2)`

`(f \circ \: g)(x) = f(g(x))`

`(f \circ \: g)(x) = f(1 - {x}^(2) )`

`(f \circ \: g)(x) = \sqrt{(1 - {x}^(2) ) - 3}`

`(f \circ \: g)(x) = \sqrt{ - {x}^(2) - 2}`

This function is defined if and only if

`- {x}^(2) - 2 \geqslant 0`

`{x}^(2) + 2 \leqslant 0`

There is no real values that satisfies this inequality, because

`{x}^(2) + 2`

is always positive.

The domain of this composite function is a null set.